Moving the Decimal Point to Divide

Date: 02/28/2009 at 21:44:50
From: Patty
Subject: decimal point
In the problem 100 divided by .4 I know you move the decimal over to
make it 4 to solve the the problem. My question is why do we move the
decimal.
I just know it is the rule of thumb (if you will) to do this, I just
don't know the reason why it has to be moved.

Date: 02/28/2009 at 22:15:26
From: Doctor Douglas
Subject: Re: decimal point
Hi Patty,
It's not a rule of thumb--it is just one of the many possible choices
of ways to evaluate this fraction.
100 / .4 = (100 * 10)/(.4 * 10) = 1000 / 4
which is a form that is a little more familiar. Multiplying top and
bottom by the same number doesn't change the value of the fraction, so
we chose a convenient number (10) to multiply by, and this is
equivalent to moving the decimal point over for both top and bottom.
We could have multiplied or divided by whatever number happens to be
convenient (but 10 is often a good choice because the multiplications
are easy). Here's an example where we might choose something different:
111/.25
We could multiply top and bottom by 100, leading to 11100/25, and
then we have a division operation still left to do. But instead, we
could have multiplied the top and bottom by 4, and this is nice
because 4*(.25) = 1.0, so this choice leads to
444/(1.0) = 444.
Please write back if you need more help with this.
- Doctor Douglas, The Math Forum
http://mathforum.org/dr.math/